Implications of energy balance non-closure on carbon dioxide flux uncertainties: Insights from large eddy simulations in convective boundary layers

• Relations between the energy flux imbalance and Fc imbalance are evaluated. • The storage induced by entrainment can be a leading factor in Fc imbalance. • The energy flux imbalance and Fc imbalance are correlated when they share the same causative mechanisms. • Energy balance closure-based adjustment methods cannot be applied to the Fc imbalance. The non-closure of surface energy balance, often encountered in eddy covariance (EC) measurements, raises a critical query: does this non-closure lead to underestimated scalar fluxes, particularly CO 2 flux (Fc), when using the same theoretical framework in EC? To address this question, we utilize high-resolution large-eddy simulations (LESs) to explore correlations between energy flux imbalances and Fc imbalances in convective boundary layers, considering both homogeneous and idealized heterogeneous surfaces. Our findings reveal that the unsteady CO 2 or storage represents a leading factor influencing Fc imbalance, especially notable when the entrainment ratio for Fc is large. Even in scenarios with uniform surface Fcs, heterogeneous thermally-generated turbulence resulting from variable surface sensible heat flux (H) can induce substantial horizontal flux divergence, magnifying Fc imbalance. While a linear correlation between the energy flux imbalance and Fc imbalance arises under shared causative mechanisms (e.g., storage), complex correlations emerge if their influencing factors differ, contingent upon surface heterogeneity and site location. This complexity underscores the limitations in applying the closing methods for energy flux imbalance to the Fc imbalance.